Convertible vehicles are known in which the top has a sunroof part in its front region. The sunroof part is displaceable to the rear with respect to the surrounding top regions. To open the entire top, the sunroof part is initially opened while the rest of the top remains closed. After the sunroof reaches its completely open position, the top is then moved to an open convertible position. The sunroof part is moved to the rear to make it possible to clear obstacles, for instance of rear headrests, while the top is opening. However, this results in the sunroof part being in a position that is unfavorable for stowage. The opened top has a large longitudinal length. This in particular is true when the sunroof has a relatively large front to back length and/or a very large opening path, which is desirable for a good open-air feeling even with an otherwise closed top.